Hi
I would say yes, you need that core.
First, a lifecast would be the ideal. All the rest will be eyeballing and random and hard to get a nice snugy fit.
You can prepare clay sheets with the thickness you want the mask to have. Place/press/adapt them in the mold, close it and fill the resulting void with plaster. Then you will have a core as a result. Make sure you prepare some kind of reference to your mold so it sits in place.
Take in account this way you will have to fill in the whole mold in one batch. And that the whole bulk must fit in your oven.
You can also make two core molds, one for each part. Same method but each half separate. This way you will have two smaller molds to fill. Also your mold reference keys will be the reference for the core mold. You could fill them separate and the glue both parts.
Plaster is the cheaper method, can be done with other materials but plaster would be ideal to start, plus a porous material is the best for both latex and foam latex.
But these methods will carry along eyeballing, and trial and error. The correct way is sculpting on a lifecast and using it as a core. You could try using a plaster head and trying to place it someway in the mold. But again trial and error and random results..